Poisson image deblurring with frame-based nonconvex regularization

Abstract

Poisson image deblurring, which aims to restore the latent image from its blurred and noisy observation, has drawn significant attention in image processing. Due to its ill-posed nature, enhancing image quality often involves incorporating a well-defined prior to effectively regularize the ill-posed inverse problem. Building upon the framelet system, we propose a frame-based nonconvex regularization method for Poisson image deblurring. The method is formulated by combining a data-fitting term with the difference of two norms, namely ℓ1 and ℓ2, on the latent image. We solve the optimization problem by combining the difference of convex functions algorithm (DCA) with the alternating direction method of multipliers (ADMM), establishing its convergence. We further employ a simulated annealing procedure and show that proposed algorithm almost certainly converges to a global minimum. Two different approaches are employed to handle the frame-based ℓ1 norm within the ADMM framework. In particular, the frame-based nonconvex regularization method is also considered for the blind Poisson problem. An effective recovery model and its algorithm are presented. Experimental results demonstrate the effectiveness of our proposed models compared with other models in terms of quantitative metrics and visual quality.